Related papers: Learning Dissipative Neural Dynamical Systems

Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…

Distributed learning is the problem of inferring a function in the case where training data is distributed among multiple geographically separated sources. Particularly, the focus is on designing learning strategies with low computational…

Understanding the learning dynamics of neural networks is one of the key issues for the improvement of optimization algorithms as well as for the theoretical comprehension of why deep neural nets work so well today. In this paper, we…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…

A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

The simulation of driven dissipative quantum dynamics is often prohibitively computation-intensive, especially when it is calculated for various shapes of the driving field. We engineer a new feature space for representing the field and…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning…

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…

We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

While a lot of progress has been made in recent years, the dynamics of learning in deep nonlinear neural networks remain to this day largely misunderstood. In this work, we study the case of binary classification and prove various…

In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones. Besides making a theoretical analysis of their expressivity, we…

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…

Robust imitation learning seeks to mimic expert controller behavior while ensuring stability, but current methods require accurate plant models. Here, robust imitation learning is addressed for stabilizing poorly modeled plants with linear…

Most stochastic gradient descent algorithms can optimize neural networks that are sub-differentiable in their parameters; however, this implies that the neural network's activation function must exhibit a degree of continuity which limits…

Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to…

Recurrent neural networks (RNNs) trained on neuroscience-inspired tasks offer powerful models of brain computation. However, typical training paradigms rely on open-loop, supervised settings, whereas real-world learning unfolds in…